#include <iostream>
#include <cmath>

using namespace std;

#include <Eigen/Core>
#include <Eigen/Geometry>

using namespace Eigen;

// 本程序演示了 Eigen 几何模块的使用方法

int main(int argc, char **argv) {

  // Eigen/Geometry 模块提供了各种旋转和平移的表示
  // 3D 旋转矩阵直接使用 Matrix3d 或 Matrix3f
  Matrix3d rotation_matrix = Matrix3d::Identity();
  // 旋转向量使用 AngleAxis, 它底层不直接是Matrix，但运算可以当作矩阵（因为重载了运算符）
  AngleAxisd rotation_vector(M_PI / 4, Vector3d(0, 0, 1));     //沿 Z 轴旋转 45 度
  cout.precision(3);
  cout << "rotation matrix =\n" << rotation_vector.matrix() << endl;   //用matrix()转换成矩阵
  // 也可以直接赋值
  rotation_matrix = rotation_vector.toRotationMatrix();
  // 用 AngleAxis 可以进行坐标变换
  Vector3d v(1, 0, 0);
  Vector3d v_rotated = rotation_vector * v;
  cout << "(1,0,0) after rotation (by angle axis) = " << v_rotated.transpose() << endl;
  // 或者用旋转矩阵
  v_rotated = rotation_matrix * v;
  cout << "(1,0,0) after rotation (by matrix) = " << v_rotated.transpose() << endl;

  // 欧拉角: 可以将旋转矩阵直接转换成欧拉角
  Vector3d euler_angles = rotation_matrix.eulerAngles(2, 1, 0); // ZYX顺序，即roll pitch yaw顺序
  cout << "yaw pitch roll = " << euler_angles.transpose() << endl;

  // 欧氏变换矩阵使用 Eigen::Isometry (homogenious)
  Isometry3d T = Isometry3d::Identity();                // 虽然称为3d，实质上是4＊4的矩阵
  T.rotate(rotation_vector);                                     // 按照rotation_vector进行旋转
  T.pretranslate(Vector3d(1, 3, 4));                     // 把平移向量设成(1,3,4)
  cout << "Transform matrix = \n" << T.matrix() << endl;

  // 用变换矩阵进行坐标变换
  Vector3d v_transformed = T * v;                              // 相当于R*v+t
  cout << "v tranformed = " << v_transformed.transpose() << endl;

  // 对于仿射和射影变换，使用 Eigen::Affine3d 和 Eigen::Projective3d 即可，略

  // 四元数
  // 可以直接把AngleAxis赋值给四元数，反之亦然
  Quaterniond q = Quaterniond(rotation_vector);
  cout << "quaternion from rotation vector = " << q.coeffs().transpose()
       << endl;   // 请注意coeffs的顺序是(x,y,z,w),w为实部，前三者为虚部
  // 也可以把旋转矩阵赋给它
  q = Quaterniond(rotation_matrix);
  cout << "quaternion from rotation matrix = " << q.coeffs().transpose() << endl;
  // 使用四元数旋转一个向量，使用重载的乘法即可
  v_rotated = q * v; // 注意数学上是qvq^{-1}
  cout << "(1,0,0) after rotation = " << v_rotated.transpose() << endl;
  // 用常规向量乘法表示，则应该如下计算
  cout << "should be equal to " << (q * Quaterniond(0, 1, 0, 0) * q.inverse()).coeffs().transpose() << endl;

  return 0;
}

#include <iostream>
#include <iomanip>

using namespace std;

#include <Eigen/Core>
#include <Eigen/Geometry>

using namespace Eigen;

#include <pangolin/pangolin.h>

struct RotationMatrix {
  Matrix3d matrix = Matrix3d::Identity();
};

ostream &operator<<(ostream &out, const RotationMatrix &r) {
  out.setf(ios::fixed);
  Matrix3d matrix = r.matrix;
  out << '=';
  out << "[" << setprecision(2) << matrix(0, 0) << "," << matrix(0, 1) << "," << matrix(0, 2) << "],"
      << "[" << matrix(1, 0) << "," << matrix(1, 1) << "," << matrix(1, 2) << "],"
      << "[" << matrix(2, 0) << "," << matrix(2, 1) << "," << matrix(2, 2) << "]";
  return out;
}

istream &operator>>(istream &in, RotationMatrix &r) {
  return in;
}

struct TranslationVector {
  Vector3d trans = Vector3d(0, 0, 0);
};

ostream &operator<<(ostream &out, const TranslationVector &t) {
  out << "=[" << t.trans(0) << ',' << t.trans(1) << ',' << t.trans(2) << "]";
  return out;
}

istream &operator>>(istream &in, TranslationVector &t) {
  return in;
}

struct QuaternionDraw {
  Quaterniond q;
};

ostream &operator<<(ostream &out, const QuaternionDraw quat) {
  auto c = quat.q.coeffs();
  out << "=[" << c[0] << "," << c[1] << "," << c[2] << "," << c[3] << "]";
  return out;
}

istream &operator>>(istream &in, const QuaternionDraw quat) {
  return in;
}

int main(int argc, char **argv) {
  pangolin::CreateWindowAndBind("visualize geometry", 1000, 600);
  glEnable(GL_DEPTH_TEST);
  pangolin::OpenGlRenderState s_cam(
    pangolin::ProjectionMatrix(1000, 600, 420, 420, 500, 300, 0.1, 1000),
    pangolin::ModelViewLookAt(3, 3, 3, 0, 0, 0, pangolin::AxizY)
  );

  const int UI_WIDTH = 500;

  pangolin::View &d_cam = pangolin::CreateDisplay().
    SetBounds(0.0, 1.0, pangolin::Attach::Pix(UI_WIDTH), 1.0, -1000.0f / 600.0f).
    SetHandler(new pangolin::Handler3D(s_cam));

  // ui
  pangolin::Var<RotationMatrix> rotation_matrix("ui.R", RotationMatrix());
  pangolin::Var<TranslationVector> translation_vector("ui.t", TranslationVector());
  pangolin::Var<TranslationVector> euler_angles("ui.rpy", TranslationVector());
  pangolin::Var<QuaternionDraw> quaternion("ui.q", QuaternionDraw());
  pangolin::CreatePanel("ui").SetBounds(0.0, 1.0, 0.0, pangolin::Attach::Pix(UI_WIDTH));

  while (!pangolin::ShouldQuit()) {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    d_cam.Activate(s_cam);

    pangolin::OpenGlMatrix matrix = s_cam.GetModelViewMatrix();
    Matrix<double, 4, 4> m = matrix;

    RotationMatrix R;
    for (int i = 0; i < 3; i++)
      for (int j = 0; j < 3; j++)
        R.matrix(i, j) = m(j, i);
    rotation_matrix = R;

    TranslationVector t;
    t.trans = Vector3d(m(0, 3), m(1, 3), m(2, 3));
    t.trans = -R.matrix * t.trans;
    translation_vector = t;

    TranslationVector euler;
    euler.trans = R.matrix.eulerAngles(2, 1, 0);
    euler_angles = euler;

    QuaternionDraw quat;
    quat.q = Quaterniond(R.matrix);
    quaternion = quat;

    glColor3f(1.0, 1.0, 1.0);

    pangolin::glDrawColouredCube();
    // draw the original axis
    glLineWidth(3);
    glColor3f(0.8f, 0.f, 0.f);
    glBegin(GL_LINES);
    glVertex3f(0, 0, 0);
    glVertex3f(10, 0, 0);
    glColor3f(0.f, 0.8f, 0.f);
    glVertex3f(0, 0, 0);
    glVertex3f(0, 10, 0);
    glColor3f(0.2f, 0.2f, 1.f);
    glVertex3f(0, 0, 0);
    glVertex3f(0, 0, 10);
    glEnd();

    pangolin::FinishFrame();
  }
}

#include <iostream>
#include <Eigen/Core>
#include <Eigen/Geometry>

using namespace std;

int main(int agrc, char **argv){

// put xiaoluobo first data
    Eigen::Quaterniond q1 (0.35, 0.2, 0.3, 0.1);
    Eigen::Vector3d t1 (0.3,0.1,0.1);

    // put xiaoluobo second data
    Eigen::Quaterniond q2 (-0.5,0.4,-0.1,0.2);
    Eigen::Vector3d t2 (-0.1,0.5,0.3);

    // input xiaoluobo first observation point data
    Eigen::Vector3d p (0.5,0,0.2);
    Eigen::Vector3d o;

    // initialize eular matrix
    Eigen::Isometry3d T_1cw = Eigen::Isometry3d::Identity();
    Eigen::Isometry3d T_2cw = Eigen::Isometry3d::Identity();

    // start to solve problem
    // normalization
    q1.normalize();
    q2.normalize();

    // output data q1,q2 after normalization

    cout<<"q1="<<endl<<q1.x()<<endl<<q1.y()<<endl<<q1.z()<<endl<<q1.w()<<endl;
    cout<<"q2="<<endl<<q2.x()<<endl<<q2.y()<<endl<<q2.z()<<endl<<q2.w()<<endl;

    //  quaternion and displacement(homogenious matrix)

    T_1cw.rotate(q1);
    T_1cw.pretranslate(t1);

    T_1cw.rotate(q2);
    T_1cw.pretranslate(t2);

    cout << "T_1cw:" << endl << T_1cw.matrix() << endl;
    cout << "T_2cw:" << endl << T_2cw.matrix() << endl;

    // get o coordinate

    o = T_2cw * T_1cw.inverse() * p;

    // output o coordinate

    cout << "o= " << o.transpose() << endl;
    return 0;
}